15. A and B together take 5 days to do a work, B
and C take 7 days to do the same and A and C
take 4 days to do it. Who among these will take
the least time, if put to do it alone?
(a) A
(b) B
(c) C
(d) data is not adequate
16. A tap can empty a tank in one hour. A second
tap can empty it in 30 minutes. If both the taps
operate simultaneously, how much time is
needed to empty the tank?
(a) 20 min.
(c) 40 min.
(b) 30 min.
(d) 45 min.
Answers
Answer:
15. (a) A
16. (a) 20 min.
Step-by-step explanation:
15) A and B together take 5 days to do a work
Work done by A and B in 1 day = A + B = 1/5 → ( 1 )
B and C takes 7 days to do the same work
Work done by B and C in 1 day = B + C = 1/7 → ( 2 )
A and C takes 4 days to do it
Work done by A and C in 1 day = A + C = 1/4 → ( 3 )
Adding all the 3 equations ( 1 ), ( 2 ) and ( 3 )
⇒ 2( A + B + C ) = 1/5 + 1/7 + 1/4
⇒ 2( A + B + C ) = ( 28 + 20 + 35 )/140
⇒ 2( A + B + C ) = 83/140
⇒ A + B + C = 83/280
Work done by all together in one day= 83/280
Work done A in one day = Work done by all together in one day - Work done by B + C in one day = 83/280 - 1/7 = ( 83 - 40 )/280 = 43/280
∴ A can complete the work in 280/43 or 6.5 days
Work done by B in one day = Work done by all together in one day - Work done by A + C in one day = 83/280 - 1/4 = ( 83 - 70 )/280 = 13/280
∴ B can finish the work in 280/13 or 21.5 days
Work done by C in one day = Work done by all together in one day - Work done by A + B in one day = 83/280 - 1/5 = ( 83 - 56 )/280 = 27/280
∴ C takes 280/27 or 10.3 days to complete the work.
Hence A takes least time to finish the work ( Option a ).
16) A tap can empty the tank in 1 hour i.e 60 minutes
Work done by a tap to empty the tank in one minute = 1/60
Second tap can empty the tank in 30 minutes
Work done by second tap to empty the tank in 1 minute = 1/30
If both the taps work together
Work done by both the taps in one minute = 1/60 + 1/30 = ( 1 + 2 )/60 = 3/60 = 1/20